Finned Compact Heat Exchangers.
Heat Exchanger (HEX) size and weight with gas flows are typically limited by the low conductivity of the gas and resulting lower gas side heat transfer coefficients. In these cases, the surface area of plates that separate the fluids, or bound the source of heat (e.g. electronics component) or cooling, is insufficient to meet performance requirements. Fins are added to the separating plate, or primary surface area, to add surface area and reach out into the gas flow. This facilitates the flow of heat from the gas to the separating plate. Fins can increase surface area exposed to the gas by multiple factors. In fact, in some examples, fins represent over 80% of the available surface area. While the fins provide enhanced surface area and heat transfer, the added area also adds weight, volume, pressure drop and cost. Therefore, fin configurations need to be carefully chosen to optimize heat transfer while minimizing volume, weight, pressure drop and cost.
Thermal Efficiency (TE), which is the ratio of the heat transfer coefficient to the friction, or pressure drop, factor, is an important measure of heat exchanger performance, since there is always a tradeoff between heat transfer effectiveness and pumping power losses. Pumping power losses are a serious limitation in many cases. Therefore, a fin configuration that minimizes pressure drop, or pumping power, for a given heat transfer is highly desired. In these cases, the HEX can be made more compact (lower volume and higher face velocity cases), without causing excessive pumping power. Table 1 lists the thermal efficiencies of several conventional fins, including plain plate, perforated plate, wavy plate, and louvered fins. The thermal efficiency (TE) in the table is defined as the heat transfer Stanton (St) number times Prandtl (Pr) number, to the two-thirds power, over the friction (f) coefficient. The non-dimensional St and Pr combination is a measure of the heat transfer for the fin configuration of interest, with the non-dimensional f playing a similar role for pressure drop. Plain plate fins are very simple, and relatively easy to form. The perforated fin requires that small holes be formed in the plain plate fin, which makes this fin more expensive. The wavy fin configuration doesn't require holes, but special tooling is required to form the wavy surfaces that need to be fitted between separation plates, or on tubes. Lastly, louvered fins are the most complex to form and probably the most expensive.
Plain fins simply increase the amount of surface area exposed to the gas, and through heat conduction to the fluid in adjoining tubes or channels, increase the heat transfer. Well-known formulas can be used to define the effectiveness of the increased fin surface area, or fin efficiency. With the plain fin, a boundary layer develops on the plate that has a high heat transfer coefficient at the front of the plate where the boundary layer starts and is very thin. However, the coefficient drops substantially with distance, as the boundary layer thickens. On average, the heat transfer coefficient is then relatively low over the whole plate. With perforated fins, the smooth boundary layer of the plain fin becomes interrupted at the perforations. As the boundary layer restarts at each perforation, the heat transfer coefficient again reaches a locally high level. With the constant restarting of the boundary layer, the average heat transfer coefficient is increased over that for the plain fin. This is very beneficial. However, because of the restarting of the boundary layer, friction, or pressure drop, also increases. However, the net overall effect is beneficial, as noted by the TE value in Table 1. As shown, the perforated plate fin has the best Thermal Efficiency (TE) of all of the cases. Therefore, for a given pressure drop, perforated plates would produce the highest heat transfer.
TABLE 1Comparison of Fin Thermal Efficiencies atReynolds Number of 1000Fin TypeThermal Efficiency (StPr2/3/f)Plain Plate0.283Perforated Plate0.338Wavy Plate0.182Louvered Plate0.236
Wavy wall and louvered fin thermal efficiencies are not as high as that for the perforated fin, as indicated in Table 1. It is speculated that the disruption of the boundary layer in the perforated fin case is modest, and the overall pressure drop, consisting of both form (i.e. fluid separation zones) and surface friction contributions, is not significantly increased versus the plain plate fin case. The net result is a higher heat transfer than a plain fin and only modestly higher pressure drop, giving enhanced thermal efficiency. In contrast, the louvered fins have substantial protrusions into the flow. These create substantial flow disruptions and flow separation. Heat transfer is increased as a result of these disruptions. However, pressure drop is also substantially increased, resulting in a net reduction of thermal efficiency. For the wavy wall case, flow separations can also be induced as the flow moves over the “waves”, resulting in improved heat transfer, but also a reduction in thermal efficiency relative to the perforated plate case. In conclusion, the perforated plate yields the best thermal efficiency, as a result of boundary layer disruption, but not bulk flow disruption. This high thermal efficiency is important to controlling pressure drop in compact HEXs.
As noted above, for optimal thermal efficiency, the boundary layer along the fin should be disrupted, but large scale flow disruptions should be avoided. The greater the frequency of boundary layer disruption, the higher the average heat transfer coefficient, for a nearly fixed thermal efficiency. Therefore, a plate with many perforations might be best. However, it is difficult to form many perforations, and fin cost could substantially increase.
Foam-Based Heat Exchangers.
As noted above, compact finned heat exchangers are well developed and proven, but they do not offer heat transfer and pressure drop performance that can meet advanced cooling or heating requirements. To achieve goals for these applications, substantial advances are required in heat exchanger materials and configurations. As a significant departure from compact finned heat exchangers, open cell metal and graphite foams have been put forward as advanced thermal management solutions for challenging applications, such as fusion reactors. An open cell foam structure viewed in close-up shows small structures in the open cell foam that adds substantial surface area for heat transfer. While offering orders of magnitude increases in surface area and heat transfer capability, these materials have correspondingly much higher pressure drop than is desired for many applications. Also, these materials have very thin ligaments that connect with the adjoining tubes or channels that contain the heat transfer fluids. This limits the effectiveness of the high surface area by bottle-necking the flow of heat to the fluid. The result is a lower thermal efficiency compared to the fin configurations listed in Table 1. In addition, these materials are very expensive.
What is needed is a new material that has the heat transfer performance of open-celled foams, with a pressure drop that is much lower per heat transferred, as well as a lower volume, weight, and a much lower cost.